Untestable Properties in the Kahr-Moore-Wang Class

Jordan, Charles; Zeugmann, Thomas

doi:10.1007/978-3-642-20920-8_19

Cited by 2 publications

(5 citation statements)

References 18 publications

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“…Finally, we simplified the untestable property of Alon et al [2] and showed that there are untestable properties of directed graphs expressible with quantifier prefixes ∀ 3 ∃, ∀ 2 ∃∀, ∀∃∀ 2 , and ∀∃∀∃. Recently, we have shown in Jordan and Zeugmann [27] that there are untestable properties of directed graphs expressible with prefix ∀∃∀, improving on three of these prefixes.…”

Section: Discussionmentioning

confidence: 80%

“…We have recently shown that one can express untestable graph properties with prefix ∀∃∀ (improving on prefixes ∀ 2 ∃∀, ∀∃∀ 2 , and ∀∃∀∃ from this paper), see Jordan and Zeugmann [27]. This prefix was first studied by Kahr, Moore and Wang [28].…”

Section: Introductionmentioning

confidence: 82%

“…We have recently shown that there are untestable graph propertie in this class, see Jordan and Zeugmann [27]. It is again trivial to prove that [∀∃∀, (0, 1)] does not have the finite model property.…”

Section: Untestable Classesmentioning

confidence: 99%

“…In Jordan and Zeugmann [27], we improved on some of the prefixes of this paper and showed that [∀∃∀, (0, 1)] = is untestable.…”

Section: Previous Work On the Classificationmentioning

confidence: 99%

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Testable and untestable classes of first-order formulae

Jordan

Zeugmann

2012

Journal of Computer and System Sciences

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In property testing, the goal is to distinguish structures that have some desired property from those that are far from having the property, based on only a small, random sample of the structure. We focus on the classification of first-order sentences according to their testability. This classification was initiated by Alon et al. [2], who showed that graph properties expressible with prefix ∃ * ∀ * are testable but that there is an untestable graph property expressible with quantifier prefix ∀ * ∃ * . The main results of the present paper are as follows. We prove that all (relational) properties expressible with quantifier prefix ∃ * ∀∃ * (Ackermann's class with equality) are testable and also extend the positive result of Alon et al.[2] to relational structures using a recent result by Austin and Tao [8]. Finally, we simplify the untestable property of Alon et al. [2] and show that prefixes ∀ 3 ∃, ∀ 2 ∃∀, ∀∃∀ 2 and ∀∃∀∃ can express untestable graph properties when equality is allowed.

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Section: Discussionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 82%

Section: Untestable Classesmentioning

confidence: 99%

“…In Jordan and Zeugmann [27], we improved on some of the prefixes of this paper and showed that [∀∃∀, (0, 1)] = is untestable.…”

Section: Previous Work On the Classificationmentioning

confidence: 99%

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Testable and untestable classes of first-order formulae

Jordan

Zeugmann

2012

Journal of Computer and System Sciences

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“…Finally, we thank Hiro Ito for pointing out an omission in a previous version of the proof of Lemma 2 (cf. Jordan and Zeugmann (2011)). …”

Section: Acknowledgmentsmentioning

confidence: 99%

The Kahr-Moore-Wang Class Contains Untestable Properties

Jordan¹,

Zeugmann²

2016

BJMC

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Abstract. Property testing is a kind of randomized approximation in which one takes a small, random sample of a structure and wishes to determine whether the structure satisfies some property or is far from satisfying the property. We focus on the testability of classes of first-order expressible properties, and in particular, on the classification of prefix-vocabulary classes for testability. The main result is the untestability of [∀∃∀, (0, 1)]=. We also show that this class remains untestable without equality in at least one model of testing. These classes are well-known and (at least one is) minimal for untestability. We discuss what is currently known about the classification for testability and briefly compare it to other classifications.

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Untestable Properties in the Kahr-Moore-Wang Class

Cited by 2 publications

References 18 publications

Testable and untestable classes of first-order formulae

Testable and untestable classes of first-order formulae

The Kahr-Moore-Wang Class Contains Untestable Properties

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